Rapidity distribution of pseudoscalar Higgs boson to NNLO$_{A}$ + $\bar{N}$$\bar{N}$$\bar{L}$$\bar{L}$

We present the differential predictions for the rapidity distribution of pseudoscalar Higgs boson through gluon fusion at the LHC. These results are obtained taking into account the soft-virtual (SV) as well as thenext-to-soft virtual (NSV) resummation effects to next-to-next-to-leading-logarithmic (NNLL) accuracy and matching them to the approximate fixed order next-to-next-to-leading-order (NNLO$_A$) computation. We perform the resummation in two-dimensional Mellin space by limiting ourselves to the contributions only from gluon-gluon (gg) initiated channels. The NNLO$_A$rapidity distribution of pseudoscalar Higgs is
obtained by applying a ratio method on the NNLO rapidity distribution of the scalar Higgs boson. We also present the first analytical results of N$^3$LO rapidity distribution of pseudoscalar Higgs at SV + NSV accuracy. The phenomenological impacts of NNLO$_A$ + $\overline{NNLL}$ predictions for 13 TeV LHC are studied. We observe that for m$_A$ =125(700) GeV the SV + NSV resummation at the NNLL level brings about 14.76% (11.48%) corrections to the NNLO$_A$ results at the central scale value of μ$_R$= μ$_F$=m$_A$. Further, we find that the sensitivity to the renormalization scale gets improved substantially by the inclusion of NSV
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resummed predictions at NNLL accuracy.